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Unformatted text preview: on we are going to look at a method for getting a rough sketch of a general
polynomial. The only real information that we’re going to need is a complete list of all the zeroes
(including multiplicity) for the polynomial.
In this section we are going to either be given the list of zeroes or they will be easy to find. In the
next section we will go into a method for determining a large portion of the list for most
polynomials. We are graphing first since the method for finding all the zeroes of a polynomial
can be a little long and we don’t want to obscure the details of this section in the mess of finding
the zeroes of the polynomial.
Let’s start off with the graph of couple of polynomials. Do not worry about the equations for these polynomials. We are giving these only so we can use
them to illustrate some ideas about polynomials.
First, notice that the graphs are nice and smooth. There are no holes or breaks in the graph and
there are no sharp corners in the graph. The graphs of polynomials will always be nice smooth
curves.
Secondly, the “humps” where the graph changes...
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